Chapter 1.2 MatrixAlgebra

P 1 1 outline matrices matrix algebra matrix

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Unformatted text preview: wi · vj = aip bpj . p =1 (1) Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose Properties of Matrix Multiplication Theorem Let A be an n × m matrix, B an m × k matrix, and C a k × l matrix, and let λ ∈ R be a scalar. Then we have the following. 1 In general, AB = BA. 2 (AB )C = A(BC ). 3 If B and C are the same size, then A(B + C ) = AB + AC . 4 If A and B are the same size, then (A + B )C = AC + BC . 5 λ(AB ) = (λA)B = A(λB ). Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose Matrix Equations Consider a linear system of equations of the form: a11 x1 + a12 x2 + · · · a21 x1 + a22 x2 + · · · . . .. . . . . . an 1 x 1 + an 2 x 2 + · · · + a1m xm = b1 + a2m xm = b2 . . . . . . + anm xm = bn This system has matrix of coefficients: a11 a12 · · · a1m a21 a22 · · · a2m A= . . . .. . . . . . . . an1 an2 · · · anm Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

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